Mathlib Map

Theorems · Definition · global analysis

IsManifold.maximalAtlas

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {H : Type u_3} →
            [inst_3 : TopologicalSpace H] →
              ModelWithCorners 𝕜 E H →
                WithTop ℕ∞ →
                  (M : Type u_4) → [inst : TopologicalSpace M] → [ChartedSpace H M] → Set (OpenPartialHomeomorph M H)

The maximal atlas of M for the C^n manifold with corners structure corresponding to the model with corners I.

Defined in
Mathlib.Geometry.Manifold.IsManifold.Basic
Cited by
65 results in Mathlib
Foundations
Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsManifold.chart_mem_maximalAtlas · cited by 24IsManifold.chart_mem_maxi…ModelWithCorners.contDiffOn_extendCoordChange · cited by 7ModelWithCorners.contDiff…Manifold.IsImmersionAtOfComplement.mk_of_continuousAt · cited by 7IsImmersionAtOfComplement…IsManifold.subset_maximalAtlas · cited by 6IsManifold.subset_maximal…Manifold.LiftSourceTargetPropertyAt.codChart_mem_maximalAtlas · cited by 5LiftSourceTargetPropertyA…Manifold.LiftSourceTargetPropertyAt.domChart_mem_maximalAtlas · cited by 5LiftSourceTargetPropertyA…contMDiffOn_symm_of_mem_maximalAtlas · cited by 5contMDiffOn_symm_of_mem_m…contMDiffAt_of_mem_maximalAtlas · cited by 4contMDiffAt_of_mem_maxima…contMDiffOn_of_mem_maximalAtlas · cited by 4contMDiffOn_of_mem_maxima…contMDiffWithinAt_iff_of_mem_maximalAtlas · cited by 4contMDiffWithinAt_iff_of_…Manifold.IsImmersionAtOfComplement.domChart_mem_maximalAtlas · cited by 4IsImmersionAtOfComplement…ModelWithCorners.contDiffWithinAt_extendCoordChange · cited by 3ModelWithCorners.contDiff…Manifold.IsImmersionAtOfComplement.codChart_mem_maximalAtlas · cited by 3IsImmersionAtOfComplement…Manifold.IsSubmersionAtOfComplement.codChart_mem_maximalAtlas · cited by 3IsSubmersionAtOfComplemen…Manifold.IsSubmersionAtOfComplement.domChart_mem_maximalAtlas · cited by 3IsSubmersionAtOfComplemen…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldENat · cited by 4985ENatWithTop · cited by 3754WithTopModelWithCorners · cited by 2462ModelWithCornersChartedSpace · cited by 2397ChartedSpaceOpenPartialHomeomorph · cited by 664OpenPartialHomeomorphcontDiffGroupoid · cited by 28contDiffGroupoidStructureGroupoid.maximalAtlas · cited by 28StructureGroupoid.maximal…IsManifold.maximalAtlasCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by70

Results whose statement or proof uses this declaration.